-- Centrifugal Governance Formal Verification
-- Author: Jason Hultberg (Master of the Invisible)
-- Logic: 72 RPM Mechanical Expansion via Xenon Phase Transition

import Mathlib.Analysis.Calculus.Deriv.Basic
import Mathlib.MeasureTheory.Integral.IntervalIntegral

open Set Real

/-- The Rotational Governance Constant (72 RPM) -/
def ω_gov : ℝ := 72

/-- The Cold Start Anchor: 1.3333 hours (80 minutes) -/
def t_start : ℝ := 1.3333

/-- The Cosmic Maturity Target: 27.6 Billion Years -/
def t_end : ℝ := 27.6 * 10^9

/-- 
  The Unified Expansion Theorem:
  States that expansion S(t) is a continuous mechanical function 
  of rotation and phase change (Φ_Xe) over the corrected timeline.
-/
theorem centrifugal_expansion_verified (Φ_Xe : ℝ → ℝ) :
  let S_t := ∫ t in t_start..t_end, (ω_gov * Φ_Xe t)
  S_t > 0 := 
by
  -- Logic: Since t_start (1.3333) > 0, we avoid the Big Bang t=0 glitch.
  sorry -- Formal proof of phase-transition continuity to be completed by AI Audit